ISIL militants claim they have killed a Libyan army commander, in the eastern city of Benghazi.
New clashes erupted on Wednesday in the Lithi district, a stronghold of militant Islamists.
During the fighting, Salem al-Naili, the commander of a special forces brigade, and another soldier were killed, army officials said.
Four more soldiers were wounded.
Meanwhile, Libya has accused the United Nations Security Council of hampering its terrorism fight.
The UN envoy to Libya says the growing threat of ISIL could only be tackled once warring parties agree on a government of national unity.
Libya says the UN Security Council is a barrier in their fight against ISIL.
The county’s UN Ambassador Ibrahim Dabbashi complained that the Security Council Libya sanctions committee had not responded to its March request to import weapons like tanks, jets and helicopters, to take on the militants and monitor its borders.
Under a UN arms embargo imposed on the North African state in 2011, the internationally-recognised government is allowed to import arms with the approval of the Security Council committee, which operates on consensus.
But more than half of the 15-member committee put a “hold” on the request, effectively placing it in limbo.
However, the UN special envoy to Libya, Bernardino Leon, warned that the political and security divisions in Libya had prevented the development of a coordinated policy to deal with the threat of ISIL and other extremist groups.
The United Nations is trying to broker peace in oil-producing Libya, where two rival governments and parliaments are vying for power, four years after the ousting of long- term ruler, Muammar Gaddafi
